Geodesic
A lower bound on the radius of analyticity of a power series in a real Banach space
Timothy Nguyen 1
1 Department of Mathematics, 2-310 MIT 77 Massachusetts Ave. Cambridge, MA 02139, U.S.A.
Studia Mathematica, Tome 191 (2009) no. 2, pp. 171-179 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $F$ be a power series centered at the origin in a real Banach space with radius of uniform convergence $\varrho$. We show that $F$ is analytic in the open ball $B$ of radius $\varrho/\sqrt{e}$, and furthermore, the Taylor series of $F$ about any point $a \in B$ converges uniformly within every closed ball centered at $a$ contained in $B$.
DOI : 10.4064/sm191-2-5
Keywords: power series centered origin real banach space radius uniform convergence varrho analytic ball radius varrho sqrt furthermore taylor series about point converges uniformly within every closed ball centered contained nbsp

Timothy Nguyen  1

1 Department of Mathematics, 2-310 MIT 77 Massachusetts Ave. Cambridge, MA 02139, U.S.A. 
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Timothy Nguyen. A lower bound on the radius of analyticity of a power series in a real Banach space. Studia Mathematica, Tome 191 (2009) no. 2, pp. 171-179. doi: 10.4064/sm191-2-5

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